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CHM 101 GAGE Mathematical Models from Scientific Data ANSWERS Suppose that you suspect that there is a relationship between the volume of a gas sample and its temperature. To investigate, you collect the following data by changing the temperature and measuring the resulting volume of the gas. Temperature (kelvins) 273 283 298 310 318 323 340 358 363 375 1. Volume (mL) 224 232 247 251 257 266 280 294 299 310 What is the independent variable in this experiment? ______temperature________ Explain. You are able to set the value of temperature so it does not depend on another variable while the volume depends on the value for the temperature so therefore it is a dependent variable. What variable(s) would you have to control in this situation? Type of gas, type of container, amount of gas, pressure 2. From a visual scan of the data decide if the relationship between temperature and volume is direct or inverse. direct If you graphed the data what would you expect to see? Straight line 3. On the graphing calculator, enter the independent variable in L1 and the dependent variable in L2. Display the graph of the data and decide if your answers to Question 2 are correct. 4. Determine the mathematical model (equation) for the relationship between temperature and volume by generating the regression equation for the data set. As you find the equation, generate the regression coefficient (r2) to determine how well the model fits the data. V = 0.839 T – 6.00 where T = temperature (K) V = volume (mL) When you use the calculator or Excel to determine a regression equation, the equation will be displayed in a general format such as y = ax + b. Since you know what the variables x and y are, and you have the values for “a” and “b”, you must rewrite the regression equation, substituting the information you have, to arrive at the correctly formatted equation. r2 = 0.995 Since r2 is close to the value of 1, most of the variation in the variable y is explained by changes in x. Therefore, the equation (model) is a good fit for the data.